1. Field of the Invention
This invention relates to MPSK symbol hypothesis testing, and, more specifically, to metrics for performing MPSK symbol hypothesis testing, and systems and methods for providing the metrics.
2. Related Art
An MPSK symbol constellation is a constellation of M possible symbols arranged around a unit circle on the quadrature (I-Q) plane. The value M is a power of two and can be expressed as M=2p. In a transmitter employing an MPSK symbol constellation, a bit to symbol mapper maps successive renderings of p bits into one of the symbols, a modulator modulates a carrier signal with the I and Q values associated with that symbol, and an antenna transmits the signal. In a receiver employing the MPSK symbol constellation, an antenna receives the signal, and a demodulator demodulates the carrier signal to baseband I and Q values. The demodulator or a downstream decoder may then perform hypothesis testing on the received symbols represented by the baseband I and Q values in order to estimate the MPSK symbols that were transmitted.
A conventional approach for performing MPSK symbol hypothesis testing is through a look up table containing entries for all possible hypotheses for all possible received symbols. For a given received symbol, a metric for a particular hypothesis is obtained by performing an access to the lookup table. Multiple accesses may be performed for each of the possible hypotheses. The metrics may then be analyzed to estimate the symbol corresponding to the most likely hypothesis.
A problem with the conventional approach is that, in certain applications, the amount of memory required may be prohibitive. Consider, for example, an application in which received symbols are represented through 8 bits of resolution, and the symbol constellation is an 8-PSK symbol constellation in which 8 hypotheses are possible for each received symbol. In this application, a lookup table with 211 entries would be required. However, space and cost constraints might not permit a lookup table of this size.